Details

sample102.0ms

Algorithm

intervals

Results

42.0ms	110×	body	1280	valid
20.0ms	69×	body	640	valid
10.0ms	256×	pre	80	true
5.0ms	29×	body	320	valid
2.0ms	41×	body	80	valid
1.0ms	7×	body	160	valid

simplify23.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	5
1	22	5
2	33	5
3	39	5
4	50	5
5	70	5
6	99	5
7	124	5
8	166	5
9	259	5
10	260	5
11	260	5

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(+ x (- (tan (+ y z)) (tan a)))
0.1b	(- (tan (+ y z)) (tan a))
3.6b	(tan (+ y z))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`prod-diff`
17×	`add-cube-cbrt`
11×	`associate-+r+`
10×	`add-log-exp`
4×	`tan-quot`
3×	`pow1` `add-exp-log` `expm1-log1p-u` `fma-def` `fma-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`sub-neg` `tan-sum` `diff-log` `sum-log` `frac-sub` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+r-` `flip3--` `flip3-+` `flip--` `flip-+` `difference-of-squares`

Counts

3 → 72

Calls

3 calls:

7.0ms	(+ x (- (tan (+ y z)) (tan a)))
8.0ms	(- (tan (+ y z)) (tan a))
4.0ms	(tan (+ y z))

series321.0ms

Counts

3 → 9

Calls

3 calls:

131.0ms	(+ x (- (tan (+ y z)) (tan a)))
129.0ms	(- (tan (+ y z)) (tan a))
61.0ms	(tan (+ y z))

simplify101.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	276	685
1	732	540
2	3128	507
3	5001	488

prune263.0ms

Filtered

81 candidates to 59 candidates (72.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (tan y) (tan z))
0.1b	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
0.1b	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
0.3b	(* (tan y) (tan z))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

151×	`*-un-lft-identity`
108×	`prod-diff`
107×	`add-sqr-sqrt`
100×	`add-cube-cbrt`
85×	`times-frac`
56×	`associate-+r+`
24×	`distribute-lft-out`
18×	`fma-neg`
14×	`associate-/r/`
13×	`add-log-exp`
8×	`flip3--` `flip--`
7×	`tan-quot` `div-inv`
6×	`pow1` `add-exp-log` `fma-def` `add-cbrt-cube`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`associate-r` `associate-l` `sum-log`
2×	`+-commutative` `sub-neg` `flip3-+` `diff-log` `flip-+` `distribute-lft-out--` `difference-of-squares`
1×	`frac-times` `associate-+r-` `associate-r/` `pow-prod-down` `associate-l/` `frac-add` `prod-exp` `*-commutative` `frac-sub` `cbrt-unprod` `unswap-sqr`

Counts

4 → 207

Calls

4 calls:

5.0ms	(+ (tan y) (tan z))
16.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
22.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
5.0ms	(* (tan y) (tan z))

series1.0s

Counts

4 → 12

Calls

4 calls:

103.0ms	(+ (tan y) (tan z))
422.0ms	(- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a))
391.0ms	(+ x (- (/ (+ (tan y) (tan z)) (- 1 (* (tan y) (tan z)))) (tan a)))
107.0ms	(* (tan y) (tan z))

simplify78.0ms

Algorithm

egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	676	4084
1	2087	3388
2	5001	3151

prune712.0ms

Filtered

219 candidates to 133 candidates (60.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (tan y) (tan z)) (* (tan y) (tan z)))
0.3b	(* (tan y) (tan z))
0.3b	(* (tan y) (tan z))
0.3b	(* (tan y) (tan z))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

49×	`pow1`
44×	`tan-quot`
22×	`add-exp-log` `add-cbrt-cube`
20×	`frac-times` `pow-prod-down`
16×	`add-sqr-sqrt`
14×	`associate-r/` `associate-l/`
11×	`prod-exp` `cbrt-unprod`
10×	`add-cube-cbrt` `-un-lft-identity` `associate-r` `associate-l*`
4×	`expm1-log1p-u` `pow-sqr` `*-commutative` `pow-prod-up` `log1p-expm1-u` `add-log-exp`
3×	`unswap-sqr`
2×	`pow-plus`
1×	`pow2` `swap-sqr`

Counts

4 → 120

Calls

4 calls:

11.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))
5.0ms	(* (tan y) (tan z))
6.0ms	(* (tan y) (tan z))
5.0ms	(* (tan y) (tan z))

series435.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(* (* (tan y) (tan z)) (* (tan y) (tan z)))
102.0ms	(* (tan y) (tan z))
105.0ms	(* (tan y) (tan z))
102.0ms	(* (tan y) (tan z))

simplify52.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	319	802
1	1443	681
2	5001	660

prune504.0ms

Filtered

132 candidates to 83 candidates (62.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* (tan y) (tan z))) (cbrt (* (tan y) (tan z))))
9.0b	(cbrt (* (tan y) (tan z)))
9.0b	(cbrt (* (tan y) (tan z)))
9.0b	(cbrt (* (tan y) (tan z)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

44×	`tan-quot`
33×	`cbrt-div`
20×	`frac-times`
14×	`associate-r/` `associate-l/`
11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`expm1-log1p-u` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 90

Calls

4 calls:

10.0ms	(* (cbrt (* (tan y) (tan z))) (cbrt (* (tan y) (tan z))))
4.0ms	(cbrt (* (tan y) (tan z)))
4.0ms	(cbrt (* (tan y) (tan z)))
4.0ms	(cbrt (* (tan y) (tan z)))

series689.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(* (cbrt (* (tan y) (tan z))) (cbrt (* (tan y) (tan z))))
167.0ms	(cbrt (* (tan y) (tan z)))
158.0ms	(cbrt (* (tan y) (tan z)))
158.0ms	(cbrt (* (tan y) (tan z)))

simplify112.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 3 (103.0ms)

Iter	Nodes	Cost
0	252	882
1	873	805
2	3829	729
3	5001	719

prune523.0ms

Filtered

102 candidates to 78 candidates (76.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.1b

regimes292.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	24
1	37	24

end0.0ms

sample3.1s

Algorithm

intervals

Results

1.7s	3974×	body	1280	valid
480.0ms	1985×	body	640	valid
359.0ms	8000×	pre	80	true
120.0ms	681×	body	320	valid
60.0ms	1089×	body	80	valid
31.0ms	271×	body	160	valid